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Syntax Definition wceq 1259
Description: Extend wff definition to include class equality.

For a general discussion of the theory of classes, see http://us.metamath.org/mpeuni/mmset.html#class.

(The purpose of introducing 
wff  A  =  B here, and not in set theory where it belongs, is to allow us to express i.e. "prove" the weq 1408 of predicate calculus in terms of the wceq 1259 of set theory, so that we don't "overload" the  = connective with two syntax definitions. This is done to prevent ambiguity that would complicate some Metamath parsers. For example, some parsers - although not the Metamath program - stumble on the fact that the  = in  x  =  y could be the  = of either weq 1408 or wceq 1259, although mathematically it makes no difference. The class variables  A and  B are introduced temporarily for the purpose of this definition but otherwise not used in predicate calculus. See df-cleq 2049 for more information on the set theory usage of wceq 1259.)

Hypotheses
Ref Expression
cA.wceq  class  A
cB.wceq  class  B
Assertion
Ref Expression
wceq  wff  A  =  B

See definition df-tru 1262 for more information.

Colors of variables: wff set class
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